**Probability And Odds Examples :**

Here we are going to see some example problems on probability.

The word odds is frequently used in probability and statistics. Odds relate the chances in favour of an event A to the chances against it. Suppose a represents the number of ways that an event can occur and b represents the number of ways that the event can fail to occur.

The odds of an event A are a : b in favour of an event and

P(A) = a/(a+b)

Further, it may be noted that the odds are a : b in favour of an event is the same as to say that the odds are b : a against the event.

If the probability of an event is p , then the odds in favour of its occurrence are p to (1− p) and the odds against its occurrence are (1− p) to p .

**Question 1 :**

A cricket club has 16 members, of whom only 5 can bowl. What is the probability that in a team of 11 members at least 3 bowlers are selected?

**Solution :**

Number of members in a club = 16

= 11 batsman + 5 bowlers

At least 3 bowlers mean, we may select 3 bowlers, 4 bowlers and 5 bowlers.

- If we select 3 bowlers out of 5, we have to choose 8 bats man out of 11.
- If we select 4 bowlers out of 5, we have to choose 7 bats man out of 11.
- If we select 5 bowlers out of 5, we have to choose 6 bats man out of 11.

Probability of getting 3 bowlers and 8 bats man

= (^{5}C_{3 }⋅ ^{11}C_{8}) / ^{16}C_{11 } --------(1)

Probability of getting 4 bowlers and 5 bats man

= (^{5}C_{4 }⋅ ^{11}C_{7}) / ^{16}C_{11} --------(2)

Probability of getting 5 bowlers and 6 bats man

= (^{5}C_{5 }⋅ ^{11}C_{6}) / ^{16}C_{11} --------(3)

(1) + (2) + (3)

= (1650 + 1650 + 462) / 4368

= 3762/4368

= 627/728

**Question 2 :**

(i) The odds that the event A occurs is 5 to 7, find P(A).

(ii) Suppose P(B) = 2/5. Express the odds that the event B occurs.

**Solution :**

(i) P(A) = a/(a+b)

= 5/(5+7)

= 5/12

(ii) Suppose P(B) = 2/5. Express the odds that the event B occurs.

Note :

If the probability of an event is p , then the odds in favour of its occurrence are p to (1− p).

By using the point given in note, we may find the answer.

= (2/5) to 1 - (2/5)

= (2/5) to (3/5)

= 2 to 3.

Hence the answer is 2 to 3.

After having gone through the stuff given above, we hope that the students would have understood, "Probability And Odds Examples"

Apart from the stuff given in "Probability And Odds Examples", if you need any other stuff in math, please use our google custom search here.

Widget is loading comments...

You can also visit our following web pages on different stuff in math.

**WORD PROBLEMS**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Time and work word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**