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Q.

Two unbiased coins are tossed simultaneously, then the probability of getting no head is $A B,$ then $(A + B) 2$ is equal to

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a

10

b

20

c

16

d

25

answer is D.

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Detailed Solution

Given, two unbiased coins are tossed simultaneously.
The probability of an event to be occurred is the division of the number of favourable outcomes by the total number of outcomes that is,

Probability of an event = Number of favourable cases Total number of cascs

Finding the total number of possible outcomes.
The possible outcomes are hh, ht, th and tt where h stands for head and t for tail.
So, the total number of possible outcomes is 4.
Finding the number of favourable outcomes.
The favourable outcome is that no head is obtained if the event tt occurs.
So, the number of favourable outcomes is 1.
Find the required value by using the formula of probability that is,

Probability of an event = Number of favourable cascs Total number of cascs Probability = 14 A B = 14

So, the values of a and b are 1 and 4 respectively.
Now,

(A + B) 2 = (1 + 4) 2 = 52 = 25

Thus, the required value of

A + B 2

is 25.
Hence, the correct option is 4.

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