(a) In a game, a fair die is rolled once and two unbiased coins are tossed at once. What is the probability of obtaining 3 and a tail? (b) A box contains 10...
Question 1 Report
(a) In a game, a fair die is rolled once and two unbiased coins are tossed at once. What is the probability of obtaining 3 and a tail?
(b) A box contains 10 marbles, 7 of which are black and 3 are red. Two marbles are drawn one after the other without replacement. Find the probability of getting:
(i) a red, then a black marble ; (ii) two black marbles.
Answer Details
(a) \(P(\text{rolling a }3)=\tfrac16\). For two coins, \(P(\text{at least one tail})=1-P(HH)=1-\tfrac14=\tfrac34\). These are independent, so \[P(3\text{ and a tail})=\frac16\times\frac34=\frac{3}{24}=\frac18.\]
(b) \(10\) marbles: \(7\) black, \(3\) red, drawn without replacement.
- (i) Red then black: \[\frac{3}{10}\times\frac{7}{9}=\frac{21}{90}=\frac{7}{30}.\]
- (ii) Two black: \[\frac{7}{10}\times\frac{6}{9}=\frac{42}{90}=\frac{7}{15}.\]
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