Browsing as Guest. Progress, bookmarks and attempts are disabled.
Log in to track your work.
Feb/Mar 2019 p62 q1
2598
On each day that Tamar goes to work, he wears either a blue suit with probability 0.6 or a grey suit with probability 0.4. If he wears a blue suit then the probability that he wears red socks is 0.2. If he wears a grey suit then the probability that he wears red socks is 0.32.
(i) Find the probability that Tamar wears red socks on any particular day that he is at work.
(ii) Given that Tamar is not wearing red socks at work, find the probability that he is wearing a grey suit.
Solution
(i) The probability that Tamar wears red socks is calculated by considering both cases: wearing a blue suit and wearing a grey suit.
Probability of wearing red socks with a blue suit: \(0.6 \times 0.2 = 0.12\).
Probability of wearing red socks with a grey suit: \(0.4 \times 0.32 = 0.128\).
Total probability of wearing red socks: \(0.12 + 0.128 = 0.248\).
Expressed as a fraction: \(\frac{31}{125}\).
(ii) We need to find the probability that Tamar is wearing a grey suit given that he is not wearing red socks.
Probability of not wearing red socks with a blue suit: \(0.6 \times 0.8 = 0.48\).
Probability of not wearing red socks with a grey suit: \(0.4 \times 0.68 = 0.272\).
Total probability of not wearing red socks: \(0.48 + 0.272 = 0.752\).
Using Bayes' theorem, the probability of wearing a grey suit given not wearing red socks is:
