When 5 fair coins are tossed simultaneously, in how many outcomes will

Question

When 5 fair coins are tossed simultaneously, in how many outcomes will the first and the last coin turn up heads?

A. 1
B. 3
C. 8
D. 31
E. 30

IanStewart · Accepted Answer

When you toss five different coins, for each coin 2 things can happen, so a total of (2)(2)(2)(2)(2) = 2^5 = 32 things can happen.

The first coin will be heads 1/2 of the time, and the last coin will be heads 1/2 of the time, so they will be both be heads (1/2)(1/2) = 1/4 of the time. That is, in 1/4 of all outcomes, the first and last coin are heads. So the answer is (1/4)*32 = 8.

EMPOWERgmatRichC · Answer

Hi All,

With 5 coins being tossed, you might expect this question to be more difficult than it actually is. The prompt asks for the number of outcomes in which the first and fifth coins are both heads. To start, we can 'lock in' those options.

H _ _ _ H

Now we just have to focus on the possible outcomes for the remaining 3 coins. Mathematically, since each coin has 2 possible outcomes, there are (2)(2)(2) = 8 options.

You could also 'map out' the possibilities:
HHH
HHT
HTH
THH

TTT
TTH
THT
HTT

8 total options.

Final Answer:  C

GMAT assassins aren't born, they're made,
Rich

mathivanan · Answer

Total outcome is 2^5 = 32
Favourable cases = H_ _ _ H
The second, third, and fourth places can be occupied by either H or T
There are 2^3 =8 ways that can be done.
Hence, the correct option is C

Dinesh8y · Answer

H _ _ _ H
So, only 03 options of Heads/ Tails, each place has 2 options, so 2x2x2=8

ScottTargetTestPrep · Answer

If we flip 5 coins, we see that the total number of possible outcomes is 2 x 2 x 2 x 2 x 2 = 32, if there are no restrictions. In this problem, however, the first coin must be heads, so there is only 1 possible outcome for the first coin, and the 5th coin must also be heads, so there is only 1 possible outcome for the 5th coin.

The 2nd, 3rd, and 4th coins can be either heads or tails, so there are 2 possible outcomes for each of these coins.

Thus, the total number of ways to flip 5 coins, with the first and fifth coins turning up heads, is 1 x 2 x 2 x 2 x 1 = 8.

Answer: C

Pritishd · Answer

Approach - I (Slot Method)  
Applying the slot method, the outcome for the first and last slots is predefined to be heads, hence we only need to compute the outcome for the slots in between

1   2   2   2   1  = 1 * 2 * 2 * 2 * 1 = 8

A fair coin can have at most 2 outcomes i.e. heads and tails and hence the 2 in the above approach

Approach - II (Listing Method)

1. HHHHH
2. HHHTH
3. HHTHH
4. HTHHH
5. HTTHH
6. HHTTH
7. HTHTH
8. HTTTH

Ans.  C

bumpbot · Answer

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When 5 fair coins are tossed simultaneously, in how many outcomes will

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When 5 fair coins are tossed simultaneously, in how many outcomes will

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