Two equally likely bags each contain 10 balls. B1 has 7 red and 3 green; B2 has 3 red and 7 green. A randomly drawn ball is red. Find the probability it came from B1, to one decimal place.
Bayes’s rule gives $P(B1|R)=P(R|B1)P(B1)/P(R)$. Here $P(R)=0.7(0.5)+0.3(0.5)=0.5$. Therefore $P(B1|R)=0.7(0.5)/0.5=0.7$. The equal bag sizes and equal bag-selection probabilities are both used.
More Probability and statistics: Random variables, normal, Poisson and binomial distributions, sampling from distributions, conditional probability and Bayes' theorem, mean, median, mode, standard deviation and variance questions
GATE 2026 IN Q31– A data set is given to be [1, 2, 0, −1, −3, 1, 2, 0, 1]. The median of the data set is .…
GATE 2026 IN Q36– A box contains three apples and two oranges. Two fruits are removed randomly in…
GATE 2025 IN Q52– The probability of a student missing a class is 0.1. In a total number of 10 classes, the…
GATE 2024 IN Q35– Indian Premier League has divided the sixteen cricket teams into two equal pools: Pool-A…
GATE 2024 IN Q65– A random variable X has density f X(x)=e-x for x0 and zero otherwise. The probability…
GATE 2023 IN Q32– A discrete random variable X takes values 0, 1, 2, with P(X=0)=0.25 and P(X=1)=0.5. If E[]…