Problem

5. I have two coins. One is fair, and has a probability of coming up heads of.5.
The second is bent, and has a probability of coming up heads of. 75 .
If I toss each coin once, what is the probability that at least one of the coins will come up tails?
0.375
0.625
0.874
1.0

Answer

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Answer

Final Answer: The probability that at least one of the coins will come up tails is \(\boxed{0.625}\).

Steps

Step 1 :We have two coins. One is fair, and has a probability of coming up heads of 0.5. The second is bent, and has a probability of coming up heads of 0.75.

Step 2 :If we toss each coin once, we want to find the probability that at least one of the coins will come up tails.

Step 3 :The probability of at least one coin coming up tails is the complement of the probability of both coins coming up heads.

Step 4 :The probability of both coins coming up heads is the product of the individual probabilities of each coin coming up heads.

Step 5 :So, we need to calculate the product of the probabilities of each coin coming up heads, and then subtract this from 1 to find the probability of at least one coin coming up tails.

Step 6 :Let's denote the probability of the fair coin coming up heads as \(p_{\text{heads, fair}} = 0.5\) and the probability of the bent coin coming up heads as \(p_{\text{heads, bent}} = 0.75\).

Step 7 :The probability of both coins coming up heads is \(p_{\text{both heads}} = p_{\text{heads, fair}} \times p_{\text{heads, bent}} = 0.375\).

Step 8 :Finally, the probability of at least one coin coming up tails is \(p_{\text{at least one tails}} = 1 - p_{\text{both heads}} = 0.625\).

Step 9 :Final Answer: The probability that at least one of the coins will come up tails is \(\boxed{0.625}\).

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