-->

Probability

Question
CBSEENMA12033798

Find the probability distribution of the number of tails when three coins are tossed.

Solution

Here X denotes the number of tails obtained in three tosses of a coin. Thus X can take the values 0, 1, 2, 3.
Let p be the probability of getting tail and q be the probability of not getting a tail.
therefore space space space space straight p space equals space 1 half comma space space space straight q space equals space 1 minus space straight p space equals space 1 space minus space 1 half space equals space 1 half
straight P left parenthesis straight X space equals space 0 right parenthesis space equals space straight q space straight q space straight q space space equals space 1 half cross times 1 half cross times 1 half space equals space 1 over 8
straight P left parenthesis straight X space equals space 1 right parenthesis space equals space straight p space straight q space straight q space space plus space straight q space straight p space straight q space plus space straight q space space straight q space straight p
space space space space space space space space space space space space space space space space space space equals space 1 half cross times 1 half cross times 1 half plus 1 half cross times 1 half cross times 1 half plus 1 half cross times 1 half cross times 1 half space equals space 1 over 8 plus 1 over 8 plus 1 over 8 equals space 3 over 8
straight P left parenthesis straight X space equals space 2 right parenthesis space equals space straight p space straight p space straight q space plus space straight p space straight q space straight p space space plus space straight q space straight p space space straight p
equals space 1 half cross times 1 half cross times 1 half plus 1 half cross times 1 half cross times 1 half plus 1 half cross times 1 half cross times 1 half space equals space 1 over 8 plus 1 over 8 plus 1 over 8 equals space 3 over 8
straight P left parenthesis straight X space equals 3 right parenthesis space equals space straight p space straight p space straight p space equals space 1 half cross times 1 half cross times 1 half space equals 1 over 8
space space space space space space space space space space space space
∴ probability distribution table is

         

Some More Questions From Probability Chapter