Let E1 be the event that tails come up when the coin is tossed the first time and E2 be the event that heads come up when the coin istossed the second time. Drag the probability values from the right column and drop them in the corresponding events in the left column.Notp(E₁) and p(E₂)p(E₁ ∩ E₂)Independence1/21/41/61/361/16IndependentNot independent1/21/41/61/361/16IndependentNot indepen
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Let E1 be the event that tails come up when the coin is tossed the first time and E2 be the event that heads come up when the coin is
tossed the second time. Drag the probability values from the right column and drop them in the corresponding events in the left column.
Not
p(E₁) and p(E₂)
p(E₁ ∩ E₂)
Independence
1/2
1/4
1/6
1/36
1/16
Independent
Not independent
1/2
1/4
1/6
1/36
1/16
Independent
Not independent
Explanation:
Intuitively, these should be independent, since the first event seems to have no influence on the second. In fact we can compute as
follows:
First p(E1) = 1/2 and p(E2) = 1/2 by the symmetry of coin tossing. Furthermore, E1 E2 is the event that the first two coins come up tails
and heads, respectively. Since there are four equally likely outcomes for the first two coins (HH, HT, TH, and TT ), p(E1 E2) = 1/4.
p(E1 E2) = 1/4 = (1/2) · (1/2) = p(E1) p(E2). So, the events are independent.
Hint #1
References
References
Hints
26. Award: 10.00 points Problems? Adjust credit for all students. Required information
Let E1 be the event that the first coin comes up tails and E2 be the event that two, and not three, heads come up in a row. Drag
the probability values from the right column and drop them in the corresponding events in the left column.
Not
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