**Probability Questions for Grade 11 :**

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

Let S be the sample space associated with a random experiment and A be an event. Let n(S) and n(A) be the number of elements of S and A respectively. Then the probability of the event A is defined as

P(A) = n(A)/n(S)

= Number of cases favourable to A/Exhaustive number of cases in S

**Question 1 :**

What is the chance that (i) non-leap year (ii) leap year should have fifty three Sundays?

**Solution :**

Number of days in non leap year = 365

= 52 week + 1 day

= 52 Sundays + 1 day

Number of Sundays in a year = 52

Days in a week = { Sunday, Monday, Tuesday, Wednesday, Thursday, Saturday }

n(S) = 7

(i) Let "A" be the event of getting the probability of 53 Sundays in a year.

n(A) = 1

P(A) = n(A) / n(S)

= 1/7

(ii) Let "B" be the event of getting the probability of 53 Sundays in a leap year.

Number of days in leap year = 366 days

= 364 days + 2 days

= 52 Sundays + 2 days

Chance of being 53 Sundays = {(Sun, mon),(mon, tue), (tue, wed), (wed, thur) (thur, fri) (fri, sat) (sat, sun)}

B = {(Sun, mon), (sat, sun)}

n(B) = 2

P(B) = n(B) / n(S)

P(B) = 2/7

**Question 2 :**

Eight coins are tossed once, find the probability of getting (i) exactly two tails (ii) at least two tails (iii) at most two tails

**Solution :**

**When eight coins are tossed, number of events will be = 2 ^{8 } = 256**

**n(S) = 256**

**(i) Let "A" be the event of getting two tails.**

**n(A) = ^{ 8}c_{2}**

** n(A) = (8 **⋅ 7)/(2 ⋅ 1)

n(A) = 28

P(A) = n(A) / n(S)

= 28 / 256

= 7/64

(ii) at least two tails

**Let "B" be the event of getting at least two tails.**

**At least two tails means, we may get 2 tails, 3 tails so on up to 8 tails.**

**Other wise,**

= 1 - P(Getting lesser than two tails)

= 1 - [P(0 tail) + P(1 tail)]

= 1 - [(** ^{8}c_{0}/256) + **(

** = 1 - [(1/256) + (8/256)]**

** = 1 - (9/256)**

** = (256 - 9) / 256**

** = 247 / 256**

(iii) at most two tails

Let "C" be the event of getting at most two tails.

**At most two tails means, we may get 0 tail, 1 tail and 2 tails.**

** = P(0 tail) + ****P(1 tail) + ****P(1 tails)**

** = **(** ^{8}c_{0}/256) + **(

** = (1/256) + (8/256) + (28/256)**

** = 37/256**

After having gone through the stuff given above, we hope that the students would have understood, "Probability Questions for Grade 11"

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