A weighted coin has the property that the Heads comes up 60 percent of the time. On two flips of the coin, is it more likely that the outcomes from the two flips are the same, or the outcomes from the two flips are different?
The same outcome is more likely
Different outcomes are more likely
Likelihood is the same
Cannot determine
Explain your answer.
pr(H,H)=.6*.6= .36
pr(T,H)= .4*.6=.24
Pr(H,T)=.24
Pr(T,T)=.16
so the likelyhood of one head and one tail is .48, the probablity of both the same is .36+.16=.52
To determine whether it is more likely that the outcomes from two flips of a weighted coin are the same or different, we need to analyze the probabilities of each outcome.
Let's consider the outcomes from each flip individually:
- Probability of getting Heads (H) on a single flip: 60% (0.6)
- Probability of getting Tails (T) on a single flip: 40% (0.4)
Now, let's analyze the possible outcomes from two flips:
1. Same outcome (HH or TT):
- Probability of getting HH: (0.6 * 0.6) = 0.36 (36%)
- Probability of getting TT: (0.4 * 0.4) = 0.16 (16%)
2. Different outcomes (HT or TH):
- Probability of getting HT: (0.4 * 0.6) = 0.24 (24%)
- Probability of getting TH: (0.6 * 0.4) = 0.24 (24%)
From the calculations above, we can see that the probability of getting the same outcome (HH or TT) is higher (0.36 + 0.16 = 0.52 or 52%) than the probability of getting different outcomes (HT or TH, 0.24 + 0.24 = 0.48 or 48%).
Therefore, the answer is that it is more likely for the outcomes from two flips of the weighted coin to be the same rather than different.