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1)Find the probability for the experiment of drawing two marbles (without replacement) from a bag containing three green, four yellow, and five red marbles such that the marbles are different...

1)Find the probability for the experiment of drawing two marbles (without replacement) from a bag containing three green, four yellow, and five red marbles such that the marbles are different colors.
2)What is the probability for the experiment of tossing a coin four times and getting at least two heads. 11/16, 1/2, 13/16, 7/8, or 5/8.
3)Find the magnitude and direction angle of v=6(cos80degi+sin80degj)
4)Lauren is pulling on a trunk with a 15-N force. Wayne pulls at right angles to Lauren. With how much force must Wayne pull to make the resultant force on the trunk 22 N? Round answer to one decimal place.
5)Find the component form of v if v=2 and angle it makes with the y-axis is 120 deg.
6)Find the magnitude and direction angle of v=6i+2j
7)Find the component form of v if v=8 and angle it makes with the x-axis is 150 deg.
8)Given u=-3i-j and v=-7i+3j, find uv
9)Use the dot product to find the magnitude of u if u = (- 2, 6).
10)Find the angle between the vectors u and v if u = (1, 2) and v = (- 4, - 2).
11)u=<-3,5> and v=<4,3> solve 3u-2v
12)u=<-3,5> and v=<4,-4> solve -4u-2v
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1 Answer

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justaguide | College Teacher | (Level 2) Distinguished Educator

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1. The probability of drawing 2 marbles of different colors from a bag has to be determined given that the bag contains 3 green, 4 yellow and and five red marbles.

There are 3+4+5 = 12 marbles in the bag. The number of ways of picking 2 marbles from the bag is 12*11 = 132. The number of ways of picking 2 marbles that are the same color is 3*2 + 4*3 + 5*4 = 6 + 12 + 20 = 38. This gives the number of ways of picking 2 marbles with a different color as 132 - 38 = 94

The probability of picking two marbles with a different color is 94/132

2. When a coin is tossed there is an equal probability of getting either heads or tails and this is equal to 0.5. When a coin is tossed 4 times, the probability of getting at least 2 heads is the 1 - (probability of getting 0 heads + probability of getting 1 head) = 1 - ((1/2)^4 + (1/2)^4*4) = 1 - 5/16 = 11/16.