Question

1.1-2 A coin is tossed four times, and the sequence of heads and tails is observed. (a) List each of the 16 sequences in the outcome space $O$. (b) Let events A, B, C, and D be given by $A = { ext{at least 3 heads}}$, $B = { ext{at most 2 heads}}$, $C = { ext{heads on the third toss}}$, and $D = {1 ext{ head and 3 tails}}$. If the probability set function assigns 1/16 to each outcome in the outcome space, find (i) $P(A)$, (ii) $P(A cap B)$, (iii) $P(B)$, (iv) $P(A cap C)$, (v) $P(D)$, (vi) $P(A cup C)$, and (vii) $P(B cap D)$.

          1.1-2 A coin is tossed four times, and the sequence of heads and tails is observed.
(a) List each of the 16 sequences in the outcome space $O$.
(b) Let events A, B, C, and D be given by $A = {	ext{at least 3 heads}}$, $B = {	ext{at most
2 heads}}$, $C = {	ext{heads on the third toss}}$, and $D = {1 	ext{ head and 3 tails}}$. If the
probability set function assigns 1/16 to each outcome in the outcome space, find
(i) $P(A)$, (ii) $P(A cap B)$, (iii) $P(B)$, (iv) $P(A cap C)$, (v) $P(D)$, (vi) $P(A cup C)$, and
(vii) $P(B cap D)$.

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1.1-2 A coin is tossed four times, and the sequence of heads and tails is observed.
(a) List each of the 16 sequences in the outcome space O.
(b) Let events A, B, C, and D be given by A = extat least 3 heads, B = extat most
2 heads, C = extheads on the third toss, and D = 1 ext head and 3 tails. If the
probability set function assigns 1/16 to each outcome in the outcome space, find
(i) P(A), (ii) P(A cap B), (iii) P(B), (iv) P(A cap C), (v) P(D), (vi) P(A cup C), and
(vii) P(B cap D).

Added by Jeffrey L.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Sri K

02/14/2023

Step 1

P(A) = 1/16 P(A 0 B) = P(A) + P(B) = 1/16 + 1/16 = 1/8 Show more…

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(c) A coin is tossed three times, and the sequence of heads and tails is observed. 1.1-2 A coin is tossed four times, and the sequence of heads and tails is observed. (a) List each of the 16 sequences in the outcome space O. (b) Let events A, B, C, and D be given by A = {at least 3 heads}, B = {at most 2 heads}, C = {heads on the third toss}, and D = {1 head and 3 tails}. If the probability set function assigns 1/16 to each outcome in the outcome space, find (i) P(A), (ii) P(A ∩ B), (iii) P(B), (iv) P(A ∩ C), (v) P(D), (vi) P(A ∪ C), and (vii) P(B ∩ D).

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Transcript

00:01 It is given that a coin is taught four times and the sequence of heads and tails is not down.

00:07 So we know that when a coin is tossed in the heads or tails will be the income, which is equal to two.

00:17 So total outcomes can be calculated as niptil outcomes.

00:23 Since the coin is tossed four times, four power two, which is equal to 16 outcomes.

00:31 So the sample space will be asked.

00:33 Follows.

00:34 So this is the sample space for the given question.

00:39 So from the sample side space, so we are going to answer the questions now.

00:44 First, we are given events a.

00:47 Event a is getting at least three hex.

00:53 Getting at least three hex.

00:55 So probability of event a is.

00:58 So getting at least three hex is possible in.

01:00 This can be denoted us.

01:02 The of h greater than over equal to three.

01:04 So this is possible in 5 cases.

01:07 So 5 over total outcomes 16.

01:10 Now b is the event of getting at most 2 heads.

01:15 At most 2 heads.

01:18 So this is equal to probability of hedge less than or equal to 2.

01:24 And this is possible in 11 cases, so 11 over 16.

01:29 Next c is the event of getting head on top toss...

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