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When four coins are tossed simultaneously, in _______ number of the outcomes at most two of the coins will turn up as heads.
- a)17
- b)28
- c)11
- d)43
Correct answer is option 'C'. Can you explain this answer?
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When four coins are tossed simultaneously, in _______ number of the ou...
Explanation:
When four coins are tossed simultaneously, the total number of outcomes can be calculated using the fundamental principle of counting. For each coin, there are two possible outcomes - either a head or a tail. Since there are four coins, the total number of outcomes is 2^4 = 16.
To determine the number of outcomes where at most two of the coins will turn up as heads, we need to consider three cases:
1. All four coins are tails
2. Exactly one coin is heads
3. Exactly two coins are heads
Case 1: All four coins are tails
In this case, there is only one outcome.
Case 2: Exactly one coin is heads
There are four ways to choose which coin will be heads. For each of these choices, the remaining three coins must be tails. Therefore, there are 4 outcomes in this case.
Case 3: Exactly two coins are heads
There are four ways to choose which two coins will be heads. For each of these choices, the remaining two coins must be tails. Therefore, there are 6 outcomes in this case.
Adding up the outcomes from all three cases, we get a total of 1 + 4 + 6 = 11 outcomes where at most two of the coins will turn up as heads.
Therefore, the correct answer is option C) 11.
When four coins are tossed simultaneously, the total number of outcomes can be calculated using the fundamental principle of counting. For each coin, there are two possible outcomes - either a head or a tail. Since there are four coins, the total number of outcomes is 2^4 = 16.
To determine the number of outcomes where at most two of the coins will turn up as heads, we need to consider three cases:
1. All four coins are tails
2. Exactly one coin is heads
3. Exactly two coins are heads
Case 1: All four coins are tails
In this case, there is only one outcome.
Case 2: Exactly one coin is heads
There are four ways to choose which coin will be heads. For each of these choices, the remaining three coins must be tails. Therefore, there are 4 outcomes in this case.
Case 3: Exactly two coins are heads
There are four ways to choose which two coins will be heads. For each of these choices, the remaining two coins must be tails. Therefore, there are 6 outcomes in this case.
Adding up the outcomes from all three cases, we get a total of 1 + 4 + 6 = 11 outcomes where at most two of the coins will turn up as heads.
Therefore, the correct answer is option C) 11.
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Community Answer
When four coins are tossed simultaneously, in _______ number of the ou...
The question requires you to find number of the outcomes in which at most 2 coins turn up as heads i.e., 0 coins turn heads or 1 coin turns head or 2 coins turn heads. The number of outcomes in which 0 coins turn heads is 4C0 = 1 outcome. The number of outcomes in which 1 coin turns head is 4C1 = 6 outcomes. The number of outcomes in which 2 coins turn heads is,
4C2 = 15 outcomes. Therefore, total number of outcomes = 1 + 4 + 6 = 11 outcomes.
4C2 = 15 outcomes. Therefore, total number of outcomes = 1 + 4 + 6 = 11 outcomes.
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When four coins are tossed simultaneously, in _______ number of the outcomes at most two of the coins will turn up as heads.a)17b)28c)11d)43Correct answer is option 'C'. Can you explain this answer?
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