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Suppose you toss a fair coin four times and observe the sequence of heads and tails. (a) Select a sample space. What values does the probability function P assign to each of the possible outcomes? (b) Suppose you record the number of heads from the four tosses. Find the following probabilities: (i) P(four heads) (ii) P(exactly one head) (iii) P(at least three heads)

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closed as off-topic by José Carlos Santos, Saad, ArsenBerk, user91500, Shailesh Sep 16 '18 at 9:46

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  • $\begingroup$ Welcome to MSE. It will be more likely that you will get an answer if you show us that you made an effort. This should be added to the question rather than in the comments. $\endgroup$ – José Carlos Santos Sep 16 '18 at 8:01
  • $\begingroup$ Hello, I am not able to understand what a sample space means here in (a). Is (b)(i) = P(four heads) = P(Exactly one head) = P (atleast one head) = 1/64? as I believe the chances of H/T = 1/2 ? $\endgroup$ – Ritu Mathad Sep 16 '18 at 8:02
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The sample space consists of 16 different sequences and all are equally likely with a probability $=\frac{1}{16}$

Sample space $={(HHHH, HHHT, HHTH, HHTT, HTHH, HTHT, HTTH, HTTT, THHH, THHT, THTH, THTT, TTHH, TTHT, TTTH, TTTT)}$

b)

Probability of ( Four heads) $=\frac{1}{16}$

Probability of ( Exactly One head ) $=\frac{4}{16}$

Probability of (Atleast three heads) $=\frac{5}{16}$

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