wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

An urn contains 25 balls of which 10 balls bear a mark X and the remaining 15 bear a mark Y. A ball is drawn at random from the urn, its mark note down and it is replaced. If 6 balls are drawn in this way, find the probability that

The number of balls with X mark and Y mark will be equal.

Open in App
Solution

It is case of Bernoulli trials with n=6. Let success be defined as drawing a ball marked X.

p=P(a success in a single draw)=1025=25

q=125=35

Clearly, Z has a binomial distribution with n=6, p=25 and q=35

P(Z=r)=nCrprqnr=6Cr(25)r(35)6r

Required probability =P(three successes and three failures)

=P(3)=6C3p3q3=6C3(25)3(35)3=20×(25)3(35)3=20×8125×27125=8643125


flag
Suggest Corrections
thumbs-up
0
similar_icon
Similar questions
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Bayes Theorem
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon