Question

In a coin tossing experiment, if the coin shows head, 1 die is thrown and the result is recorded. But if the coin shows tail, 2 dice are thrown and their sum is recorded. What is the probability that the recorded number will be 2​

Answer 1

Given,

In a coin tossing exp,

coins shows head : 1 dice is thrown..

coin shows tail : 2 dice is thrown..

Now,

P( getting head) = 1/2

P(getting 2 on single throw of dice) = 1/6

P(getting tail) = 1/2

P(getting 2 as sum when two dice are thrown) = 1/36

So there will be two events through which the result will be calculated..

a) Getting a head and then to throw a dice to get 2.

b) Getting a tail and then throw 2 dice to get the sum of two.

So the required probability will be the sum of the probabilities..

Let R be the required probability,

R =

$\frac{1}{2} \times \frac{1}{6} + \frac{1}{2} + \frac{1}{36}$

=

$\frac{7}{72}$

=

$0.9722$

So the required probability will be 0.98.