Sam has a bag of 18 counters. The bag contains 8 black counters, 7 purple counters, and 3 pink counters. He randomly picks a counter, does not replace it, and then picks another counter. Find the probability of each event:

(a) Picking two pink counters
(b) Picking two black counters
(c) Picking a black counter and then a purple counter
(d) Picking a black counter and then a pink counter

The question pertains to the mathematics concept probability. One calculates each event by finding the likelihood of the first pick, then multiplying it by the odds of the second pick without replacement.

Explanation:

The problem relates to the field of mathematics known as probability. Here are the determinations for each event:

(a) Picking two pink counters: The probability is 3/18 * 2/17 = 1/51.
(b) Picking two black counters: The probability is 8/18 * 7/17 = 28/153.
(c) Picking a black counter and then a purple counter: The probability is 8/18 * 7/17 = 28/153.
(d) Picking a black counter and then a pink counter: The probability is 8/18 * 3/17 = 8/102 = 4/51.

It's important to remember that each event is calculated by multiplying the probability of the first draw by the probability of the second draw (which doesn't replace the first counter).

Learn more about Probability here:

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