You have a trick coin that lands on Head 70% of the time. You flip this coin twice. What is the probability you have 1 head and 1 tail?

Give the answer as a decimal ( .0.58 for a probability of 58%)

Question

You have a trick coin that lands on Head  70% of the time.  You flip this coin twice.  What is the probability you have 1 head and 1 tail?

Give the answer as a decimal ( .0.58 for a probability of 58%)

BlackTom AI · Accepted Answer

The problem asks for the probability of getting exactly one head in two flips using a trick coin that lands heads with probability 0.7. 
First, recognize that there are two distinct orders that yield exactly one head: Head then Tail (HT) and Tail then Head (TH).
Next, compute the probability of each sequence assuming independence between flips: P(HT) = P(H) * P(T) = 0.7 * 0.3 = 0.21, since P(T) = 1 - P(H) = 0.3.
Similarly, P(TH) = P(T) * P(H) = 0.3 * 0.7 = 0.21.
Since these two sequences are disjoint events, add their probabilities to get the total probability of exactly one head: 0.21 + 0.21 = 0.42.
Expressed as a decimal, the probability is 0.42.

ERMCPS5350_003_2025_3 - INTRO TO QUANTITATIVE RISK MANAGEMENT 5. Quiz for Class 5

You have a trick coin that lands on Head 70% of the time. You flip this coin twice. What is the probability you have 1 head and 1 tail? Give the answer as a decimal ( .0.58 for a probability of 58%)

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