CFA Practice Question

There are 410 practice questions for this study session.

CFA Practice Question

A coin is tossed five times. What is the probability of obtaining exactly three heads?
A. 3/16
B. 1/4
C. 5/16
Explanation: Probability of 3 events occurring in 5 trials:

Combination of 3 events in 5 trials * (outcome for each event)x * (outcome for each event)(n-x)
where:
Combination of 3 events in 5 trials = n! / (x! * (x-1)!)
= 5! / (3! * 2!) = 120 / 12 = 10

Probability = 10 * (1/2)3 * (1/2)(5-3) = 5/16

User Contributed Comments 9

User Comment
chuong Bernoulli trials: (nCr)*(P^x)*[(1-p)^(n-x)] = (5!/2!3!)*0.5^3 x (1-0.5)^2 = 5/16
fahad SO the answer will be the same if the probability was to obtain exactly two heads instead of three?
whoi Fahad: Yes, you don't a calculation to prove this, just remember that coin toss always is backed by probabilities of 50% for each outcome.

therefore the one and only term that changes is the multiplicator (10).

for exactly one head: 5
for excatly two heads: 10
for exactly three heads: 10
for exactly four heads: 5
for exactly five heads: 1
micheleus anybody can explain further?
bashg Yes if each head is called H and each tail is T, then you want to achieve 3 coin tosses in 5. The combo would look like

HHHTT. Now, there are a number of combinations of this eg HHTTH or THTHH or HTHTH etc.

The first part of the formula calculates how many combinations of this you can get ie
n!/x!(n-x)!

Then you assign probability of independent events

Probability of 3 heads is 0.5 x 0.5 x 0.5 in other words (1/2)^3
Probability of 2 tails is 0.5 x0.5 in other words (1/2)^2
Hope this helps
aakidil Its actually 2 part question always and students attempt it wrong because answer of first part is also a choice in the list just do it carefully Part 1:
identify number of combinations by nCr here n = 5 and r=3 plug in to your calc and get answer.

Part 2:
bionomial dist. asks about 3 thing
a) no. of possible combinations
b) prob. of success
c) prob. of failure

here a=10 (5C3 = 10)
b= 50%^num. of events (12.5%)
c=50%^(num. of trials - num. of events) (25%)

so 10*12.5%*25% = 31.25% which is equal to 5/16
TiredHand As its a coin and its 50:50 either way the answer can be very quickly calculated as 0.5 to the power of 5 = 0.03125
fanDango 0.03125 =/ 0.3125
birdperson 1. how many possibilities are there (2^5) = 32
2. how many combinations are there with 3 heads (5C3) = 10
3. combinations with 3 heads / total possibilities = 10/32 = 5/16
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